Combining functions, Algebra

The topic along with functions which we ought to deal with is combining functions. For the most part this means performing fundamental arithmetic (subtraction, addition, multiplication, & division) with functions. There is one new means of combing functions which we'll need to look at as well.

Let's begin with basic arithmetic of functions. Given two functions f(x) & g(x) we have the following notation & operations.

( f + g )( x) =f ( x ) + g ( x ) ( f - g )( x ) =f ( x ) - g ( x )

( fg ) ( x ) = f ( x ) g ( x ) (f /g) ( x ) = f ( x )/ g ( x )

Sometimes we will drop the ( x )part & just write down the following,

f + g = f ( x ) + g ( x ) f - g=f ( x ) - g ( x )

fg =f ( x ) g ( x ) f/g = f ( x ) /g ( x )

Note as well that we put x's in the parenthesis, however we will frequently put in numbers as well.